PSLE In the figure, NPQR is a parallelogram. LRN and MRQ are straight lines and LM = MN. ∠LMR = 31° and ∠PQR = 55°.
- Find ∠QRN.
- Find ∠RMN.
(a)
∠QRN
= 180° - 55°
= 125° (Interior angles)
(b)
∠LRM
= ∠QRN
= 125° (Vertically opposite angles)
∠MLR
= 180° - 125° - 31°
= 24° (Angles sum of triangle)
∠MNR = ∠MLR (Isosceles triangle)
∠LMN
= 180° - 24° - 24°
= 132° (Angles sum of triangle)
∠RMN
= 132° - 31°
= 101°
Answer(s): (a) 125°; (b) 101°